15A. The RothCN Model

General description

Model structure

The RothCN model is an extension of the well-established RothC model (see RothC Model Description, Rothamsted Research, 2024). It uses the same algorithms as RothC to estimate SOC turnover, and extends the calculation to include SON turnover by introducing C:N ratios to each SOM compartment. During decomposition of SOC compartments, N is released from the decomposing materials, and in the meantime is also assimilated into microbial biomass and humus according to their respective C:N ratios. The difference between N release and assimilation determines whether net mineralization or immobilization takes place.

The RothCN model distinguishes organic inputs between plant residues and manure, as the two input types have distinct C:N ratios. Each organic input material is further divided into an easily decomposable and a resistant fraction, depending on their decomposability. Therefore, RothCN maintains four distinct SOM compartments for input materials: DPM & RPM for plant residues, and DMA & RMA for manure. Additionally for manure, a small fraction is assigned for already humified material (HMA). HMA immediately becomes part of HUM once added to soil, therefore it is only considered when partitioning the input material, but not maintained as a separate SOM compartment.

Plant residues (DPM & RPM), manure (DMA & RMA), together with microbial biomass (BIO) and humus (HUM), form the decomposable SOM compartments. In each time step, a fraction of each decomposable compartment decomposes following a first-order reaction kinetics, and converts into BIO, HUM, and CO₂. The inert organic matter compartment (IOM) is immune from decomposition.

Figure 15A.1: Compartmentalization of soil organic matter pool, partition flows of input materials, and flows of decomposed organic matter between compartments in the RothCN model.

Time step

RothCN simulates SOM turnover on a monthly time step. If annual output is required, results should be aggregated at the end of each year.

Basic input data requirement

Climate data
- Monthly precipitation (mm).
- Monthly evapotranspiration (mm).
- Mean monthly air temperature (°C).

Soil data
- Topsoil thickness (cm).
- Topsoil clay content (as percentage).
- Topsoil bulk density (g cm^–3).
- Soil cover: is the soil bare or vegetated in a particular month.

Organic input data
- Monthly input of organic C and N from plant residues (kg C/N ha^–1). If only annual input is available, the annual input distributed evenly over 12 months.
- Monthly input of organic C and N from manure and other organic fertilisers (compost, sludge, etc., kg C/N ha^–1). If only annual input is available, the annual input is distributed evenly over 12 months.
- An estimate on the fractions of the DPM and RPM compartments in the incoming plant material. If not provided, default values will be used (see Table 15A.1).
- An estimate on the fractions of the DMA and RMA compartments in the incoming manure material. If not provided, default values will be used (see Table 15A.1).

Parameters

The parameter values given below are default values derived directly from the original RothC and other models, or from literature/empirical values. They may be changed when calibrating the model.

Table 15A.1: Parameters used in RothCN model.
Parameter	Description	Default value	Unit
k_DPM	1st-order decomposition rate constant of DPM compartment.	10.0	yr^–1
k_RPM	1st-order decomposition rate constant of RPM compartment.	0.3	yr^–1
k_DMA	1st-order decomposition rate constant of DMA compartment.	10.0	yr^–1
k_RMA	1st-order decomposition rate constant of RMA compartment.	0.3	yr^–1
k_BIO	1st-order decomposition rate constant of BIO compartment.	0.66	yr^–1
k_HUM	1st-order decomposition rate constant of HUM compartment.	0.02	yr^–1
f_DPM	Partition fraction of plant residue C to DPM compartment.	0.59 (annual crops) 0.20 (perennial crops)
f_RPM	Partition fraction of plant residue C to RPM compartment.	0.41 (annual crops) 0.80 (perennial crops)
f_DMA	Partition fraction of manure and compost/sludge C to DMA compartment.	0.49 (manure) 0.15 (compost/sludge)
f_RMA	Partition fraction of manure and compost/sludge C to RMA compartment.	0.49 (manure) 0.70 (compost/sludge)
f_HMA	Partition fraction of manure and compost/sludge C to HMA compartment.	0.02 (manure) 0.15 (compost/sludge)
f_BIO	Partition fraction of decomposed organic C to BIO compartment.	0.46
f_HUM	Partition fraction of decomposed organic C to HUM compartment.	0.54
ψ	Scaling factor to adjust CO₂ fraction from decomposed SOC. See Equation 15A.24.	1.670
r'_DPM	Theoretical C:N ratio of DPM.	30.0
r'_RPM	Theoretical C:N ratio of RPM ^[2].	100.0
r'_DMA	Theoretical C:N ratio of DMA.	18.0
r'_RMA	Theoretical C:N ratio of RMA ^[2].	100.0
r'_BIO	Theoretical C:N ratio of BIO.	10.0
r'_HUM	Theoretical C:N ratio of HUM.	12.0
r'_IOM	Theoretical C:N ratio of IOM.	200.0

Algorithms

Determining rate modifying factors

The rate modifying factor is determined for each month of the simulation. Rate modifying factors are calculated following standard RothC approach.

Temperature factor

The rate modifying factor for temperature is given by:

Equation 15A.1

in which T is the monthly average temperature (°C).

Moisture factor

First, the maximum topsoil moisture deficit (TSMD_max) is calculated:

Equation 15A.2

where:

	is the percentage of clay content in the soil (5% is 5, not 0.05).
	is the depth of the soil layer (cm).

Next, the accumulative TSMD (TSMD_acc) is calculated. At the beginning of the simulation, TSMD_acc is set to 0. Then, in each of the following month:

Equation 15A.3

And the moisture factor is given by:

Equation 15A.4

Soil cover factor

The soil cover factor slows decomposition if growing plants are present.

Equation 15A.5

Combined factor

The final modifying factor is calculated by multiplying all factors:

Equation 15A.6

A generic algorithm to partition N

In many calculation cases of the RothCN model, a certain amount of N must be partitioned into several compartments according to the respective C:N ratio of each compartment. As a consequence, the sum of N from relevant compartments estimated using C:N ratios may not match the amount of the available N for partitioning. Here we describe a generic algorithm to partition a fixed amount of N into any number of compartments, while keeping the relative size of each compartment.

The amount of N_total is partitioned into n compartments according to the C size (C_i=1…n) and theoretical C:N ratio (r'_i=1…n) of each compartment:

Equation 15A.7

If , the provisional size of N compartments (N'_i) must be scaled while keeping their relative proportions, i.e., for any compartments i and j:

Equation 15A.8

, and satisfies that .

For any compartment x, solve N_x and r_x:

Equation 15A.9

Derivation

Initialization of soil organic matter pool

Initializing soil organic carbon pool

At the beginning of the simulation period, the initial soil organic carbon pool (SOC_init) is primed based on soil properties:

Equation 15A.10

where:

	is the bulk density of the soil (g cm^–3).
	is the depth of the soil layer (cm).
	is the percentage of soil organic carbon content (5% is 5, not 0.05).

If soil organic matter content (SOM%) is provided, it may be multiplied by 0.5 to give SOC%.

For compartments DPM, RPM, DMA, and RMA, their respective initial size (C_init) is calculated assuming a steady state as follows. In the special case where a field has never received organic fertilisers (manure), the initial sizes of C_DMA and C_RMA should be set to 0.

Equation 15A.11

where:

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA}.
	is the average size of annual carbon input during the simulation period (kg C ha^–1 yr^–1).
	is the average rate modifying factor ( Equation 15A.6) over the simulation period.
	is the first-order decomposition rate constant of the compartment.

If crop history is available, and should be replaced with corresponding data of the years before the simulation period for better estimation.

Explanation

The steady state assumes that the C input during a time step is decomposed within the same time step, i.e., the stock remains unchanged. According to first-order reaction kinetics:

Since and ,

The initial size of IOM is estimated according to Falloon et al. (1998). IOM is excluded from SOM decomposition, therefore its size remains the same throughout the simulation.

Equation 15A.12

In the original equation, SOC is in tonne C ha^–1. Therefore, SOC_init must be converted to tonne C ha^–1, and then the result is converted back to kg C ha^–1.

After the initial sizes of input materials and IOM pools are determined, the initial sizes of the BIO and HUM pools can be calculated as:

Equation 15A.13

in which

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, IOM}.
,	are the first-order decomposition rate constants of the BIO and HUM pool, respectively.

Initializing soil mineral and organic nitrogen pool

For all SOM compartments, the initial sizes of organic N are calculated as:

Equation 15A.14

in which

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM, IOM}.
	is the theoretical C:N ratio of the i-th compartment.

If the overall soil C:N ratio is given, an extra step of mass balance check is performed, so that the sum of SON from all compartments matches the size determined from the soil C:N ratio, i.e.:

Equation 15A.15

in which

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM, IOM}.

If the mass balance check fails, SON sizes in the soil compartments must be adjusted according to Equation 15A.9.

The initial size of soil mineral and organic N pools are finally determined as:

Equation 15A.16

If measurement or estimation on soil mineral N content is available, soil mineral N pool should be primed with the measured or estimated value.

Partitioning of input materials

Partitioning of organic carbon

When an organic input material such as plant residues or manure is added, the organic carbon in the input material is partitioned into relevant compartments according to their respective fractions.

Equation 15A.17

where:

	is the respective compartment, _i ∈ {DPM, RPM, DMA, RMA, HMA}.
	is the total organic carbon content in the plant residues or manure input (kg C ha^–1).
	is the fraction of individual compartment in the input material (see Table 15A.1).

Partitioning of organic nitrogen

The size of organic nitrogen partitioned into each compartment is provisionally determined by the size of organic C and the theoretical C:N ratio.

Equation 15A.18

where:

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HMA}.
	is the theoretical C:N ratio for each compartment (see Table 15A.1).

Then, Equation 15A.9 is used to ensure that the sum of partitioned N matches the actual N content in the input materials. This balance check is performed separately for plant residues and manure:

Equation 15A.19

Decomposition of organic carbon

Decomposition of an organic carbon compartment is simulated on a monthly time step. The size of the compartment at the beginning of the month is equal to the size at the end of the previous month, plus any additional input.

The following convention to denote a time interval is used throughout all sections:

Subscript t₀ denotes the starting point of the interval,
Subscript t denotes the end point of the interval,
Subscript t – 1 denotes the end point of the previous time interval.

Equation 15A.20

where:

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.
	is the monthly organic C input (kg C ha^–1).

HMA from manure input is added into HUM.

The decomposition follows a first order reaction kinetics. The size of the compartment at the end of the month is given by:

Equation 15A.21

where:

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM};
	is the combined rate modifying factor ( Equation 15A.6),
	is the yearly 1st order decomposition rate constant (yr^–1).
	is 1/12, since k is a yearly decomposition rate.

Therefore, the amount of decomposed C is:

Equation 15A.22

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

The symbol δ denotes decomposed material.

Decomposed organic carbon from all compartments is summed up to give the overall SOC decomposition:

Equation 15A.23

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

A fraction of δSOC is lost as CO₂, and the rest remains in the soil (C_remain), and is assimilated by microorganisms (BIO) or converted to humus (HUM). The ratio of δSOC lost as CO₂ to those remained in soil (μ) is determined by the clay content of the soil:

Equation 15A.24

where:

	is a scaling factor with a default value of 1.67 for Rothamsted soils (23.4% clay).
	is the percent clay content in the soil (i.e., 23.4% is 23.4, not 0.234).

Therefore, the fraction of CO₂ emission is , and the fraction of remains in the soil and is assimilated into BIO and HUM compartments by a ratio of 0.46 and 0.54, respectively.

Equation 15A.25

Decomposition of organic nitrogen

Monthly mineral N input is added to soil mineral N pool at the beginning of the month.

Equation 15A.26

where:

is the monthly mineral N input (kg N ha^–1).

Monthly organic N input is added to the relevant compartments at the beginning of the month.

Equation 15A.27

where:

	is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.
	is the monthly organic N input to the i-th compartment (kg N ha^–1).

HMA from manure input is added into HUM.

Soil organic N pool is also updated with monthly additions:

Equation 15A.28

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.

After input addition, the actual C:N ratio of each compartment is determined:

Equation 15A.29

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

If the field has never received manure input (i.e. DMA and RMA = 0), this could lead to a division-by-zero error. Set r values of the corresponding compartments to NaN to avoid it.

After the determination of decomposed organic C in each compartment, N released during decomposition is calculated:

Equation 15A.30

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

The size of the N pool at the end of the month (N_t) is determined by:

Equation 15A.31

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

The total N released from decomposition is:

Equation 15A.32

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

δSON is further assimilated by BIO and HUM. The potential amount assimilated into each compartment is calculated as:

Equation 15A.33

where:

	is the respective compartment, BIO or HUM.
	is the potential amount of decomposed SOC assimilated by the BIO or HUM compartment ( Equation 15A.25).
	are the theoretical (see Table 15A.1) and actual C:N ratios ( Equation 15A.29) of the compartment, respectively. The lesser of the two values is used to maximize N assimilation.

The apostrophe in N'_assim denotes that its value is provisional and may subject to further adjustment (see Immobilization).

The difference between total N released from decomposition, and the N requirement for assimilation, is calculated:

Equation 15A.34

Mineralization

If N_diff > 0, then net mineralization takes place. N_diff is added to soil mineral N pool as inorganic N, and the corresponding amount is subtracted from soil organic N pool.

Equation 15A.35

Immobilization

If N_diff < 0, immobilization must take place to satisfy the N requirement by BIO and HUM assimilation. As soil microorganisms must compete with plants for N, immobilization is not able to utilize the entire soil mineral N pool. A coefficient (an arbitrary parameter for calibration, with a default value of 0.8) is applied to derive the mineral N available for immobilization.

Equation 15A.36

Full immobilization

If N_{immobilizable} ≥ |N_diff|, all N requirement for immobilization can be fulfilled. The amount of |N_diff| is deducted from soil mineral N and added to organic N pool.

Equation 15A.37

where:

is the potential N assimilation calculated by Equation 15A.33.

Partial or reduced immobilization

If N_{immobilizable} < |N_diff|, there is no sufficient N for full immobilization. One of two methods may be used to implement immobilization in this case: either N assimilation is partially fulfilled (“partial fulfillment”), or organic matter decomposition is reduced (“deferred decomposition”).

The total immobilized N (N_immob) can be determined as:

Equation 15A.38

The size of soil mineral and organic N pool after immobilization is:

Equation 15A.39

Method 1: Partial fulfillment
Method 2: Deferred decomposition

This is the current method implemented in Miterra-Europe.

In this approach, the BIO and HUM compartments will disregard their C:N ratios, and assimilate all immobilizable N. This leads to changes in C:N ratios of the BIO and HUM compartments.

The BIO compartment has priority for N assimilation over HUM. Therefore, N_immob satisfies assimilation by BIO first, and any remaining part goes into HUM.

Equation 15A.40

If :

where:

is the potential N assimilation calculated by Equation 15A.33.

This approach is currently not implemented. The description given here is so far for reference only.

In this approach, decomposition of organic matter in each soil compartment is reduced. As it is difficult to estimate new decomposition rate constant for each compartment, we opt for a “deferred decomposition” approach. The decomposition rate constants remain unchanged, instead a fraction of the source material is withheld from decomposition in the current time step, and is “deferred” for decomposition until a later iteration, as soon as there is sufficient inorganic N.

The actual N assimilated into BIO and HUM compartments are calculated as:

Equation 15A.41

where:

is the respective compartment, BIO or HUM, and

is the potential N assimilation calculated by Equation 15A.33.
The actual C assimilated into BIO and HUM compartments can be determined from C:N ratios, following the rearranged form of Equation 15A.33:

Equation 15A.42
The actual amount of decomposed SOC can be determined using an inversed form of Equation 15A.25:

Equation 15A.43
The amount of deferred SOC is then calculated as:

Equation 15A.44
The deferred SOC is partitioned into each compartment as follows:

Equation 15A.45

where:

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

Following deferred decomposition, all subsequent C and N calculations from Equation 15A.23 onwards must be rerun to produce new values. With this approach, and should be able to converge in one iteration.
Finally, the deferred C is added to the respective compartment as input in the next time step.

Equation 15A.46

Annual balance

At the end of the year, all forms of N removal from soil within the year, including gaseous emissions, surface runoff, leaching, and crop removal, are subtracted from soil minerl N pool. Any remaining soil mineral N is assumed to be completely denitrified.

Equation 15A.47

The annual changes in soil organic C and N pools can be determined as:

Equation 15A.48

where:

is the respective compartment,i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.